Sinkhorn Based Associative Memory Retrieval Using Spherical Hellinger Kantorovich Dynamics
We propose a dense associative memory for empirical measures (weighted point clouds). Stored patterns and queries are finitely supported probability measures, and retrieval is defined by minimizing a Hopfield-style log-sum-exp energy built from the debiased Sinkhorn divergence. We derive retrieval dynamics as a spherical Hellinger Kantorovich (SHK) gradient flow, which updates both support locations and weights. Discretizing the flow yields a deterministic algorithm that uses Sinkhorn potentials to compute barycentric transport steps and a multiplicative simplex reweighting. Under local separation and PL-type conditions we prove basin invariance, geometric convergence to a local minimizer...
| Authors | Aratrika Mustafi, Soumya Mukherjee |
|---|---|
| Primary category | stat.ML |
| Published | 21 March 2026 |
| Last updated at source | 21 March 2026 |
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